Decidability via the tilting correspondence
| Autor: | Kartas, Konstantinos |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Algebra & Number Theory, Volume 18 2024 No. 2 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2024.18.209 |
| Popis: | We prove a relative decidability result for perfectoid fields. This applies to show that the fields $\mathbb{Q}_p(p^{1/p^{\infty}})$ and $\mathbb{Q}_p(\zeta_{p^{\infty}})$ are (existentially) decidable relative to the perfect hull of $ \mathbb{F}_p(\!(t)\!)$ and $\mathbb{Q}_p^{ab}$ is (existentially) decidable relative to the perfect hull of $\overline{ \mathbb{F}}_p(\!(t)\!)$. We also prove some unconditional decidability results in mixed characteristic via reduction to characteristic $p$. Comment: Final version. Local improvements following suggestions from a study group that took place at Fields Institute in Fall 2021 and two referee reports |
| Databáze: | arXiv |
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